In these models, two turbulence scales are employed to represent turbulence processes. The three-dimensional primitive equations of momentum, temperature, humidity, and other scalars are solved by LES models. The comparison of numerical results with observations demonstrates the importance of the inclusion of wave-induced mixing as simulations of sea surface temperatures are significantly improved when wave-induced mixing is considered. For example, a parameterization scheme including wave-induced mixing is proposed to modify current Mellor-Yamada and K-profile parameterization turbulence models. To more realistically reproduce the upper ocean in ocean general circulation models, a number of ocean mixed layer models have been proposed. Furthermore, the principal way in which waves influence the oceanic circulation is through wave-induced vertical mixing, which is currently limited by model resolution, thus necessitating parameterization. This results in ocean mixed layer models producing too shallow mixed layer depths in high-latitude oceans (especially the Southern Ocean) and highly diffused thermoclines in tropical oceans, leading to weaker El NiƱo in climate models. These turbulence models are handicapped by the failure to include mixed layer physical processes such as BW and LC. However, most turbulence schemes such as the Mellor-Yamada or K-profile parameterizations do not account for wave processes. The importance of wave-induced mixing is demonstrated in upper-ocean mixed layer studies. Increased turbulence due to breaking waves (BW) decays following reductions in significant wave heights. The injection of turbulent kinetic energy from breaking surface gravity waves provides another significant source of upper-ocean turbulence. The depth at which LC the upper ocean is largely determined by the Stokes drift e-folding depth and the mixed layer thickness. Upper ocean turbulence is also affected by Langmuir turbulence and is primarily generated by surface waves. LC could enhance the vertical mixing and alter vertical profiles of temperature and velocity, making it crucial in upper ocean studies. As one of the most significant features of the mixed layer, LC appears as an array of alternating horizontal roll vortices, whose axes are roughly parallel to the wind direction. It is the interaction of Stokes drift with wind-driven surface shear flow that induces Langmuir circulation (LC) formation. ![]() ![]() Stokes drift also plays a role in modulating upper-ocean turbulence through large-scale Coriolis-Stokes and small-scale Stokes-vortex forces. Specifically, as wind blows over the ocean surface, momentum is transported into the ocean, resulting in enhancement of both mixing and turbulent kinetic energy. Waves play an integral part as they modulate those exchanges across the air-sea interface and consequently, their influence on mixed layer dynamics and structure cannot be ignored. The ocean mixed layer is central to heat and momentum exchange processes between the upper ocean and the atmosphere. Additionally, it is observed that breaking waves could destroy Langmuir cells mainly at the sea surface, rather than at deeper layers. As the wind speed increases, the influence depth of Langmuir circulation deepens. A series of numerical experiments with different wind intensities-induced Stokes drifts are also conducted to investigate wave-induced mixing. These experiments suggest that wave-induced mixing is more sensitive to wave heights than to the wavelength. To examine the effects of wave parameters on mixing, a series of wave conditions with varying wavelengths and heights are used to drive the model, resulting in a variety of Langmuir turbulence and wave breaking outcomes. In the wave-averaged equations, wave effects are calculated as Stokes forces and breaking waves. A Large Eddy Simulation model is applied to investigate the wave-induced mixed layer structure. Significant mixing caused by surface wave processes is missed in most parametric equations. ![]() However, present parametric equations of turbulent motions that are applied to global climate models result in systematic or substantial errors in the ocean surface boundary layer. ![]() Turbulent motions in the thin ocean surface boundary layer control exchanges of momentum, heat and trace gases between the atmosphere and ocean.
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